<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"  
  "http://www.w3.org/TR/html4/loose.dtd">  
<html > 
<head><title>2D CBS Elements</title> 
<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> 
<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> 
<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> 
<!-- html,index=2,3,next --> 
<meta name="src" content="elementlibmanual.tex"> 
<meta name="date" content="2017-12-30 16:42:00"> 
<link rel="stylesheet" type="text/css" href="elementlibmanual.css"> 
</head><body 
>
   <!--l. 1860--><div class="crosslinks"><p class="noindent">[<a 
href="elementlibmanualsu20.html" >next</a>] [<a 
href="elementlibmanualsu18.html" >prev</a>] [<a 
href="elementlibmanualsu18.html#tailelementlibmanualsu18.html" >prev-tail</a>] [<a 
href="#tailelementlibmanualsu19.html">tail</a>] [<a 
href="elementlibmanualse4.html#elementlibmanualsu19.html" >up</a>] </p></div>
   <h4 class="subsectionHead"><span class="titlemark">4.2   </span> <a 
 id="x26-900004.2"></a>2D CBS Elements</h4>
<!--l. 1861--><p class="noindent" >
   <h5 class="subsubsectionHead"><span class="titlemark">4.2.1   </span> <a 
 id="x26-910004.2.1"></a>Tr1CBS element</h5>
<!--l. 1863--><p class="noindent" >Represents the linear triangular finite element for transient incompressible flow analysis using cbs algorithm with
equal order approximation of velocity and pressure fields. Each node has 3 degrees of freedoms (two components of
velocity and pressure). The node numbering is anti-clockwise. The element features are summarized in
Table&#x00A0;<a 
href="#x26-9100360">60<!--tex4ht:ref: Tr1CBSsummary --></a>.
<!--l. 1869--><p class="indent" >   <hr class="figure"><div class="figure" 
>
                                                                                           
                                                                                           
<a 
 id="x26-9100125"></a>
                                                                                           
                                                                                           
<!--l. 1--><p class="noindent" ><img 
src="elementlibmanual-figure28.png" alt="PIC"  
>
<br /> <div class="caption" 
><span class="id">Figure&#x00A0;25: </span><span  
class="content">Tr1CBS element. Node numbering, Side numbering and definition of local edge c.s.(a).</span></div><!--tex4ht:label?: x26-9100125 -->
                                                                                           
                                                                                           
<!--l. 1877--><p class="indent" >   </div><hr class="endfigure">
<div class="center" 
>
<!--l. 1880--><p class="noindent" >
<div class="table">
<!--l. 1880--><p class="noindent" ><a 
 id="x26-9100360"></a><hr class="float"><div class="float" 
> <!--tex4ht:inline--><div class="tabular"> <table id="TBL-62" class="tabular" 
cellspacing="0" cellpadding="0" rules="groups" 
><colgroup id="TBL-62-1g"><col 
id="TBL-62-1"></colgroup><colgroup id="TBL-62-2g"><col 
id="TBL-62-2"></colgroup><tr 
class="hline"><td><hr></td><td><hr></td></tr><tr  
 style="vertical-align:baseline;" id="TBL-62-1-"><td  style="white-space:nowrap; text-align:left;" id="TBL-62-1-1"  
class="td11"><span 
class="cmbx-10">Keyword         </span></td><td  style="white-space:wrap; text-align:left;" id="TBL-62-1-2"  
class="td11"><!--l. 1880--><p class="noindent" ><span 
class="cmbx-10">Tr1CBS</span>                                                        </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-62-2-"><td  style="white-space:nowrap; text-align:left;" id="TBL-62-2-1"  
class="td11">Description          </td><td  style="white-space:wrap; text-align:left;" id="TBL-62-2-2"  
class="td11"><!--l. 1880--><p class="noindent" >linear triangular finite element for transient incompressible
flow analysis using cbs algorithm                                  </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-62-3-"><td  style="white-space:nowrap; text-align:left;" id="TBL-62-3-1"  
class="td11">Specific parameters</td><td  style="white-space:wrap; text-align:left;" id="TBL-62-3-2"  
class="td11"><!--l. 1880--><p class="noindent" >[<span 
class="cmtt-10">bsides</span>&#x00A0;#<span 
class="cmr-5">(ia)</span>] [<span 
class="cmtt-10">bcodes</span>&#x00A0;#<span 
class="cmr-5">(ia)</span>]                                       </td>
</tr><tr 
class="hline"><td><hr></td><td><hr></td></tr><tr  
 style="vertical-align:baseline;" id="TBL-62-4-"><td  style="white-space:nowrap; text-align:left;" id="TBL-62-4-1"  
class="td11">Parameters           </td><td  style="white-space:wrap; text-align:left;" id="TBL-62-4-2"  
class="td11"><!--l. 1891--><p class="noindent" >Since the problem formulation requires to evaluate some
boundary  terms,  the  element  boundary  edges  should  be
specified  as  well  as  the  types  of  boundary  conditions
applied  at  these  boundary  edges.  The  boundary  edges
(their  numbers)  are  specified  using  <span 
class="cmtt-10">bsides </span>array.  The
type  of  boundary  condition(s)  applied  to  corresponding
boundary  side  is  determined  by   <span 
class="cmtt-10">bcodes  </span>array.  The
available/supported  boundary  codes  are  following:  1  for
prescribed traction, 2 for prescribed normal velocity, 4 for
prescribed tangential velocity, and 8 for prescribed pressure.
If the element side is subjected to a combination of these
fundamental types boundary conditions, the corresponding
code is obtained by summing up the corresponding codes. </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-62-5-"><td  style="white-space:nowrap; text-align:left;" id="TBL-62-5-1"  
class="td11">Unknowns            </td><td  style="white-space:wrap; text-align:left;" id="TBL-62-5-2"  
class="td11"><!--l. 1892--><p class="noindent" >Two  velocity  components  (V_u  and  V_v)  and  pressure
(P_f) are required in each node.                                   </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-62-6-"><td  style="white-space:nowrap; text-align:left;" id="TBL-62-6-1"  
class="td11">Approximation      </td><td  style="white-space:wrap; text-align:left;" id="TBL-62-6-2"  
class="td11"><!--l. 1894--><p class="noindent" >Equal order approximation of velocity and pressure fields. </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-62-7-"><td  style="white-space:nowrap; text-align:left;" id="TBL-62-7-1"  
class="td11">Integration           </td><td  style="white-space:wrap; text-align:left;" id="TBL-62-7-2"  
class="td11"><!--l. 1895--><p class="noindent" >exact                                                                      </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-62-8-"><td  style="white-space:nowrap; text-align:left;" id="TBL-62-8-1"  
class="td11">Features              </td><td  style="white-space:wrap; text-align:left;" id="TBL-62-8-2"  
class="td11"><!--l. 1901--><p class="noindent" >Constant            boundary            tractions            are
supported<span class="footnote-mark"><a 
href="elementlibmanual27.html#fn1x0"><sup class="textsuperscript">1</sup></a></span><a 
 id="x26-91002f1"></a> .
Body loads representing the self-weight load are supported.</td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-62-9-"><td  style="white-space:nowrap; text-align:left;" id="TBL-62-9-1"  
class="td11">Status                 </td><td  style="white-space:wrap; text-align:left;" id="TBL-62-9-2"  
class="td11"><!--l. 1902--><p class="noindent" >Untested                                                                 </td></tr><tr  
 style="vertical-align:baseline;" id="TBL-62-10-"><td  style="white-space:nowrap; text-align:left;" id="TBL-62-10-1"  
class="td11"> </td>
</tr><tr 
class="hline"><td><hr></td><td><hr></td></tr><tr  
 style="vertical-align:baseline;" id="TBL-62-11-"><td  style="white-space:nowrap; text-align:left;" id="TBL-62-11-1"  
class="td11">                </td></tr></table></div>
<br /> <div class="caption" 
><span class="id">Table&#x00A0;60: </span><span  
class="content">Tr1CBS element summary</span></div><!--tex4ht:label?: x26-9100360 -->
</div><hr class="endfloat" />
</div>
</div>
                                                                                           
                                                                                           
                                                                                           
                                                                                           
   <!--l. 1908--><div class="crosslinks"><p class="noindent">[<a 
href="elementlibmanualsu20.html" >next</a>] [<a 
href="elementlibmanualsu18.html" >prev</a>] [<a 
href="elementlibmanualsu18.html#tailelementlibmanualsu18.html" >prev-tail</a>] [<a 
href="elementlibmanualsu19.html" >front</a>] [<a 
href="elementlibmanualse4.html#elementlibmanualsu19.html" >up</a>] </p></div>
<!--l. 1908--><p class="indent" >   <a 
 id="tailelementlibmanualsu19.html"></a>   
</body></html> 
